Question: (a) By branching on x 2 , use the branch-and-bound method to solve the following integer programming problem (IP): Maximize z 6x 1 + 2x

(a) By branching on x ₂, use the branch-and-bound method to solve the following integer programming problem (IP):

Maximize z 6x ₁ + 2x ₂

Subject to

5x ₁ + x ₂ ≤ 10

2x ₁ +x ₂ ≤ 9

x ₁. x ₂ ≥ 2 0; x ₁, x ₂ integer.

b) A hiker has a 5-ft backpack and needs to decide on the most valuable items to take on the hiking trip. There are three items from which to choose. Their volumes are 2, 3, and 4 ft ^3,and the hiker estimates their associated values on a scale from 0 to 100 as 30, 50, and 70, respectively. Formulate the problem as an LP model and what kind of linear programming is it?

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